\[\left(z\frac{\mathrm{d}}{\mathrm{d}z}z\right)^{n}\left(z^{a-1}U\left(a,b,z%
\right)\right)={\left(a\right)_{n}}{\left(a-b+1\right)_{n}}z^{a+n-1}U\left(a+n%
,b,z\right),\]